A toy model of climatic variability with scaling behaviour

Koutsoyiannis, D., A toy model of climatic variability with scaling behaviour, Journal of Hydrology, 322, 25–48, 2006.



It is demonstrated that a simple deterministic model in discrete time can capture the scaling behaviour of hydroclimatic processes at time scales coarser than annual. This toy model is based on a generalized "chaotic tent map", which may be considered as the compound result of a positive and a negative feedback mechanism, and involves two degrees of freedom. The model is not a realistic representation of a climatic system, but rather a radical simplification of real climatic dynamics. However, its simplicity enables easy implementation, even on a spreadsheet environment, and convenient experimentation. Application of the toy model gives traces that can resemble historical time series of hydroclimatic variables, such as temperature, rainfall and runoff. In particular, such traces exhibit scaling behaviour with a Hurst exponent greater than 0.5 and density function similar to that of observed time series. Moreover, application demonstrates that large-scale synthetic "climatic" fluctuations (like upward or downward trends) can emerge without any specific reason and their evolution is unpredictable, even when they are generated by this simple fully deterministic model with only two degrees of freedom. Obviously, however, the fact that such a simple model can generate time series that are realistic surrogates of real climatic series does not mean that a real climatic system involves that simple dynamics.

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Our works referenced by this work:

1. Koutsoyiannis, D., and D. Pachakis, Deterministic chaos versus stochasticity in analysis and modeling of point rainfall series, Journal of Geophysical Research-Atmospheres, 101 (D21), 26441–26451, 1996.
2. Koutsoyiannis, D., The Hurst phenomenon and fractional Gaussian noise made easy, Hydrological Sciences Journal, 47 (4), 573–595, 2002.
3. Koutsoyiannis, D., Climate change, the Hurst phenomenon, and hydrological statistics, Hydrological Sciences Journal, 48 (1), 3–24, 2003.
4. Koutsoyiannis, D., Hydrological statistics for engineering design in a varying climate, EGS-AGU-EUG Joint Assembly, Geophysical Research Abstracts, Vol. 5, Nice, European Geophysical Society, 2003.
5. Koutsoyiannis, D., and A. Efstratiadis, Climate change certainty versus climate uncertainty and inferences in hydrological studies and water resources management (solicited), European Geosciences Union General Assembly 2004, Geophysical Research Abstracts, Vol. 6, Nice, European Geosciences Union, 2004.
6. Rozos, E., A. Efstratiadis, I. Nalbantis, and D. Koutsoyiannis, Calibration of a semi-distributed model for conjunctive simulation of surface and groundwater flows, Hydrological Sciences Journal, 49 (5), 819–842, 2004.
7. Koutsoyiannis, D., Reliability concepts in reservoir design, Water Encyclopedia, Vol. 4, Surface and Agricultural Water, edited by J. H. Lehr and J. Keeley, 259–265, Wiley, New York, 2005.

Our works that reference this work:

1. Koutsoyiannis, D., Uncertainty, entropy, scaling and hydrological stochastics, 2, Time dependence of hydrological processes and time scaling, Hydrological Sciences Journal, 50 (3), 405–426, 2005.
2. Koutsoyiannis, D., Nonstationarity versus scaling in hydrology, Journal of Hydrology, 324, 239–254, 2006.
3. Koutsoyiannis, D., A. Efstratiadis, and K. Georgakakos, Uncertainty assessment of future hydroclimatic predictions: A comparison of probabilistic and scenario-based approaches, Journal of Hydrometeorology, 8 (3), 261–281, 2007.
4. Koutsoyiannis, D., and A. Montanari, Statistical analysis of hydroclimatic time series: Uncertainty and insights, Water Resources Research, 43 (5), W05429, doi:10.1029/2006WR005592, 2007.
5. Koutsoyiannis, D., A. Efstratiadis, N. Mamassis, and A. Christofides, On the credibility of climate predictions, Hydrological Sciences Journal, 53 (4), 671–684, 2008.
6. Anagnostopoulos, G. G., D. Koutsoyiannis, A. Christofides, A. Efstratiadis, and N. Mamassis, A comparison of local and aggregated climate model outputs with observed data, Hydrological Sciences Journal, 55 (7), 1094–1110, 2010.
7. Koutsoyiannis, D., Hurst-Kolmogorov dynamics and uncertainty, Journal of the American Water Resources Association, 47 (3), 481–495, 2011.
8. Koutsoyiannis, D., A. Christofides, A. Efstratiadis, G. G. Anagnostopoulos, and N. Mamassis, Scientific dialogue on climate: is it giving black eyes or opening closed eyes? Reply to “A black eye for the Hydrological Sciences Journal” by D. Huard, Hydrological Sciences Journal, 56 (7), 1334–1339, 2011.
9. O’Connell, P.E., D. Koutsoyiannis, H. F. Lins, Y. Markonis, A. Montanari, and T.A. Cohn, The scientific legacy of Harold Edwin Hurst (1880 – 1978), Hydrological Sciences Journal, doi:10.1080/02626667.2015.1125998, 2015.

Other works that reference this work:

1. #Huang, Z., and H. Morimoto, The temporal-spatial-fractal characters on Nino3.4 SST, Preprint Series in Mathematical Sciences, No. 2006-1, 2006.
2. Ng, W.W., U.S. Panu and W.C. Lennox, Chaos based analytical techniques for daily extreme hydrological observations, Journal of Hydrology, 342(1-2), 17-41, 2007.
3. Mackey, R., Rhodes Fairbridge and the idea that the solar system regulates the Earth's climate, Journal of Coastal Research, Special Issue 50, Proceedings ICS2007, 955- 968, 2007.
4. Lennartz, S. and A. Bunde, Distribution of natural trends in long-term correlated records: A scaling approach, Phys. Rev. E, 84 (2), 021129, DOI: 10.1103/PhysRevE.84.021129, 2011.
5. Rao, A. R., M. Azli and L. J. Pae, Identification of trends in Malaysian monthly runoff under the scaling hypothesis, Hydrol. Sci. J., 56 (6), 917–929, 2011.
6. Lennartz, S., and A. Bunde, On the estimation of natural and anthropogenic trends in climate records, Geophysical Monograph Series, 196, 177-189, 2012.
7. Fan, J., Rescaled range analysis in higher dimensions, Research Journal of Applied Sciences, Engineering and Technology, 5 (18), 4489-4492, 2013.
8. #Loukas, A., and L. Vasiliades, Review of applied methods for flood-frequency analysis in a changing environment in Greece, In: A review of applied methods in Europe for flood-frequency analysis in a changing environment, Floodfreq COST action ES0901: European procedures for flood frequency estimation (ed. by H. Madsen et al.), Centre for Ecology & Hydrology, Wallingford, UK, 2013.
9. Markovic, D., and M. Koch, Long-term variations and temporal scaling of hydroclimatic time series with focus on the German part of the Elbe River Basin, Hydrological Processes, 28 (4), 2202-2211, 2014.
10. Tamazian, A., J. Ludescher and A. Bunde, Significance of trends in long-term correlated records, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 91 (3), art. no. 032806, 10.1103/PhysRevE.91.032806, 2015.
11. Markovic, D., and M. Koch, Stream response to precipitation variability: A spectral view based on analysis and modelling of hydrological cycle components, Hydrological Processes, 29 (7), 1806-1816, 2015.

Tagged under: Climate stochastics, Hurst-Kolmogorov dynamics, Scaling, Uncertainty